1. Field of the Invention
The present invention relates to a lens system including a diffractive optical element, or DOE for short, such as one including a diffractive surface having lens action based on a diffraction phenomenon. More particularly, this invention is directed to a lens system that can be applied to a phototaking optical system for use on cameras of simple construction such as silver halide or electronic cameras, each made up of one positive lens.
2. Description of Related Art
So far, single plastic lenses have been used for inexpensive cameras represented by films equipped with lenses. As is well known in the art, however, a single lens has a limited degree of freedom in correcting for aberrations, with which nothing can be done with the exception that the bending shape of the lens is chosen to minimize spherical aberration or to eliminate lower-order aberrations. In particular, it is essentially impossible to correction for chromatic aberrations, and Petzval image surface. Therefore, several countermeasures are proposed to solve these problems. The first countermeasure is to allow the surface of the film to have a cylindrical shape, so that the influence of field curvature can be undermined. The second is to increase the F-number of the lens so that the amount of spherical aberration, etc. produced can be reduced or the focal depth can be increased, thereby undermining the influence of chromatic aberrations. The increase in the focal depth makes focusing unnecessary and, hence, makes lens manipulation easy, and cost reductions possible. The third is to make use of an aspheric surface, thereby introducing some improvements in aberrations, all but the chromatic aberrations and Petzval image surface.
A typical example of such a single lens is disclosed in JP-A-6-59188. This is explained more illustratively with reference to Example 9 of this publication. A lens exemplified in Example 9 has a focal length of 30 mm and an F-number of 9.7, and uses aspheric surfaces on both its surfaces. This publication refers to the correlation of distortion and coma with respect to lens thickness and stop spacing, and concludes that the lens thickness is made small to reduce the distortion, and the stop spacing is made large for coma correction. Other aberrations are corrected by the two aspheric surfaces. The surface of the film takes a cylindrical shape having a radius of curvature of 80 mm to 300 mm. As can be seen from FIG. 13 or an aberration diagram of JP-A-6-59188, however, the aberration corrections achieved are still less than satisfactory, because the spherical aberration is about 1.2 mm for the maximum ray height, the longitudinal chromatic aberration is about 0.8 mm for the g-line, and the chromatic aberration of magnification is about 0.15 mm for the maximum field angle. This is also true of other prior art lenses.
If it is desired to design a camera of higher performance using a lens having a small F-number and an autofocus mechanism, it would then be impossible to use a conventional single lens, thereby achieving a practically acceptable camera. This would also hold for a so-called electronic camera with a CCD element incorporated therein as an image pickup surface.
As will be described later, the present invention has for its object to achieve a single lens of higher performance and higher image quality than ever before, using a DOE.
An account will here be given of a diffractive optical element or DOE for short. The DOE is interpreted at great length in "Optics", Vol. 22, pp. 635-642, and pp. 730-737, for instance.
A conventional lens is based on refracting action at an interface of the medium, whereas the DOE is based on the diffraction of light. Now assume that light is incident on such a diffraction grating as depicted in FIG. 1. In general, the light exiting the grating upon being diffracted then satisfies the following relation: EQU sin .theta.-sin .theta.'=m.lambda./d (a)
where .theta. is the angle of incidence, .theta.' is the exit angle, .lambda. is the wavelength of the light, d is the pitch of the diffraction grating, and m is the order of diffraction. Therefore, if a ring form of diffraction grating is designed to have a proper pitch according to equation (a), it is then possible to focus light upon one point. In other words, the diffraction grating is allowed to have lens action. Here let r.sub.j and f represent the radius of a j-th grating ring and the focal length of a diffractive surface, respectively. Then, the following equatio n EQU r.sub.j.sup.2 =2j.lambda.f (b)
holds at a region to a first approximation.
For the diffraction grating, several types are proposed, for instance, an amplitude modulation type made up of a bright-and-dark ring, and a phase modulation type with a variable refractive index or optical path length. In the amplitude type of DOE, the ratio between the quantity of incident light and the quantity of light subject to first-order diffraction (hereinafter called diffraction efficiency), for instance, is at most about 6% because light of plural orders of diffraction is generated. The amplitude modulation type of DOE, even when bleached or otherwise treated for diffraction efficiency improvements, has a diffraction efficiency of at most about 34%. However, the phase modulation type of DOE, if it is of a saw-tooth shape in section, as depicted in FIG. 2(a), can have a diffraction efficiency increased to 100%. Such a DOE is called a kinoform. Here the height of each sawtooth is given by EQU h=m.lambda./(n-1) (c)
where h is the height of the sawtooth, and n is the index of refraction of the substrate material. As can again be expected from equation (c), the diffraction efficiency of 100% is achievable for only one wavelength. A kinoform element, if it is to step approximation as depicted in FIG. 2(b), is often called a binary optical element, and can be relatively easily fabricated by lithographic techniques. The binary optical element is known to have a diffraction efficiency of 81%, 95%, and 99% according to 4-, 8-, and 16-step approximation, respectively.
Several techniques are known for DOE design. However, the ultra-high index technique is used in the present invention. This procedure, for instance, is shown in "Mathematical equivalence between a holographic optical element and ultra-high index lens", J. Opt. Sos. Am. 69, 486-487, "Using a conventional optical design program to design holographic optical elements", Opt. Eng. 19, 649-653, or the like. In other words, the DOE is known to be equivalent to a diffractive surface that has a thickness of 0 and a very high index of refraction.
When the DOE is used in the form of a lens, two important features are available. One feature is that the DOE has aspheric action; if the diffraction grating is designed to have a proper pitch, light can then be completely focused upon one point. This action is tantamount to using an aspheric surface to reduce the spherical aberration to zero. Another feature is that the DOE has very large color dispersion or, in another parlance, has an Abbe's number of -3.45. Thus, the DOE produces chromatic aberrations in the opposite direction, which is tens of times as large as that produced by the refractive action of conventional material. The fact that dispersion is large offers the gravest problem when the DOE is applied to a lens system used in natural light. The index of refraction of the DOE at an arbitrary wavelength is given by the following equation (d): EQU n(.lambda.)=1+{n(.lambda..sub.0)-1}.multidot..lambda./.lambda..sub.0( d)
where X is an arbitrary wavelength, n(.lambda.) is the refractive index of the DOE at the wavelength .lambda., .lambda..sub.0 is a reference wavelength, and n(.lambda..sub.0) is the refractive index of the DOE at the wavelength .lambda..sub.0.
An example of such a DOE applied to a lens system used in natural light is known from "Hybrid diffractive-refractive lenses and achromats", Appl. Opt. 27, 2960-2971. This article gives a calculated value for the correction of chromatic aberrations made by use of a combination of a lens having an Abbe's number of -3.45 with a conventional glass lens on the basis of the principle of paraxial chromatic aberration correction. More specifically, the article discloses a lens having a convex surface on its object side and a plane surface on its image side, with a diffractive surface formed on the plane surface, and shows the achromatization of longitudinal chromatic aberration, and the remaining secondary spectrum. However, the article says nothing about chromatic aberration of magnification, and other aberrations. Nor is there any illustrative design data described therein.
WO95/18393 shows an exemplary arrangement comprising a positive meniscus lens that is convex on its subject side and a stop, with an image-side surface of the positive lens defined by a diffractive surface. According to this prior art arrangement, chromatic aberrations are corrected by use of a combination of a refractive system with a diffractive system, so that high performance can be achieved with no increase in the number of parts used. However, an arrangement set forth in the example of the aforesaid publication is poor in the ability to be formed and assembled because of small lens thickness. Another disadvantage of such an arrangement is that the overall lens length is somewhat long.
The applicant has filed a patent application, now published under JP-A-6-324262, wherein the application of a DOE to a telephoto lens is disclosed. As disclosed, a plane plate form of DOE is located in front of a conventional telephoto lens to improve the correction of chromatic aberrations. This arrangement is much more improved in terms of aberrations, but fails to take advantage of the DOE because of an increase in the number of parts involved.